2013 APTITUDE AND REASONING
2.In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1:
Based on the information; the total number of coins in the collection now becomes
A.90
B.80
C.60
D.50
Solution: a
The correct answer is A. 90.
Initially, the ratio of gold coins to non-gold coins is 1:3. This means that for every gold coin, there are 3 non-gold coins. If we let x be the number of gold coins, then the number of non-gold coins is 3x.
After 10 more gold coins are added, the ratio of gold coins to non-gold coins is 1:2. This means that for every gold coin, there are 2 non-gold coins. If we let y be the number of gold coins after 10 more gold coins are added, then the number of non-gold coins is 2y.
We can set up a system of equations to solve for x and y:
x+10=y
3x=2y
Solving for x and y, we get x=20 and y=30.
Therefore, the total number of coins in the collection now becomes 20+10+30=90
3.A gardener has 1000 plants: He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose?
A.14
B.24
C.32
D.34
Solution: b
In order to have the same number of rows and columns, the number of plants should form a perfect square. We need to find the minimum perfect square greater than or equal to 1000.
The square root of 1000 is approximately 31.62.
This means that the number of rows and columns should be at least 32.
The minimum perfect square greater than or equal to 1000 is 32^2 = 1024.
To find the minimum number of plants needed more, we subtract the total number of plants we already have (1000) from the minimum perfect square (1024):
1024 - 1000 = 24
Therefore, the minimum number of plants that the gardener needs more is 24.
The correct answer is B. 24.
4.A sum of RS. 700 has to be used to give seven cash prizes to the students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, then what is the least value of the prize?
A.RS. 30
B.RS. 40
C.RS. 60
D.RS. 80
Solution: b
Let's assume the least value of the prize is 'x' rupees. According to the given information, each prize is Rs. 20 less than its preceding prize. So, we can set up the following equation:
x + (x + 20) + (x + 40) + (x + 60) + (x + 80) + (x + 100) + (x + 120) = 700
Simplifying the equation:
7x + 420 = 700
7x = 700 - 420
7x = 280
x = 280 / 7
x = 40
Therefore, the least value of the prize is Rs. 40.
The correct answer is B. Rs. 40.
5.Out of 120 applications for a post, 70 are male and 80 have a driver's license. What is the ratio between the minimum to maximum number of males having driver's license?
A.1 to 2
B.2 to 3
C.3 to 7
D.5 to 7
Solution: c
The minimum number of males with a driver's license is 30, and the maximum number of males with a driver's license is 70. The ratio between the minimum and the maximum is 30:70 or 3:7.
To get the minimum number of males with a driver's license, we know that there are 80 people with a driver's license and 50 females. So, the minimum number of males with a driver's license is 80-50 = 30.
To get the maximum number of males with a driver's license, we know that there are 70 males. So, the maximum number of males with a driver's license is 70.
7.In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food?
A.25 days
B.20 days
C.15 days
D.10 days
Solution: d
Let's calculate the total amount of food available initially and then determine how long it would last for the increased number of soldiers.
Initially, there was enough food for 1000 soldiers for one month. Since we know the food supply was for 1000 soldiers, we can assume that the initial food supply was for 1000 soldiers for 30 days.
Therefore, the initial food supply would last for 1000 * 30 = 30,000 soldier-days.
After 10 days, 1000 more soldiers joined the garrison. So, now there are a total of 2000 soldiers.
To calculate how long the remaining food will last for 2000 soldiers, we need to determine the number of soldier-days the remaining food can support.
The remaining food supply is 30,000 soldier-days minus the food consumed by 1000 soldiers in 10 days, which is 1000 * 10 = 10,000 soldier-days.
So, the remaining food supply can support 30,000 - 10,000 = 20,000 soldier-days.
To calculate how long this remaining food supply will last for 2000 soldiers, we divide the number of soldier-days by the number of soldiers:
20,000 soldier-days / 2000 soldiers = 10 days
Therefore, the soldiers will be able to carry on with the remaining food for an additional 10 days.
The correct answer is D. 10 days.
8.The tank-full petrol in Arun's motor-cycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full petrol last?
A.5
B.6
C.7
D.8
Solution: d
If Arun uses 25% more petrol every day, then he will use 1.25 times as much petrol as he used the day before.
This means that the petrol will last for 1/1.25 = 0.8 times as long as it did before.
Since the petrol originally lasted for 10 days, it will now last for 0.8 * 10 = 8 days.
9.A person can walk a certain distance and drive back in six hours. He can also walk both ways in 10 hours. How much time will he take to drive both ways?
A.Two hours
B.Two and a half hours
C.Five and a half hours
D.Four hours
Solution: A
Let's assume the distance the person can walk in one direction is 'd'. Since the person can walk both ways in 10 hours, the time taken to walk one way is 10/2 = 5 hours.
Now, let's calculate the time taken to drive both ways. We know that the person can walk a certain distance and drive back in 6 hours. Since walking one way takes 5 hours, the time taken to drive one way is 6 - 5 = 1 hour.
To drive both ways, the person will take 1 hour to drive one way and another 1 hour to drive back. Therefore, the total time taken to drive both ways is 1 hour + 1 hour = 2 hours.
Therefore, the correct answer is A. Two hours.
10.In the figure from 1 to 4 above, two symbols are shown to change their position in a regular direction.
Following the same sequence, which one of the following will appear at the fifth stage?
Solution: b
Directions for the following 2 (two) items:
In each item, there are two sets of figures; first four figures named Problem figures and next four figures named Answer figures indicated as (a), (b), (c) and (d). The problem figures follow a particular sequence. In accordance with the same, which one of the four answer figures should appear as the fifth figure?
57.Problem figures:
Answer figures:
Solution: c
58.Problem figures:
Answer figures:
Solution: b
78.Consider the following diagrams:
x men, working at constant speed, do a certain job in y days. Which one of these diagrams shows the relation between x and y?
A.diagram I
B.diagram II
C.diagram III
D.diagram IV
Solution: d
11.Consider the following matrix:
What is the number at 'X' in the above matrix?
A.5
B.8
C.9
D.11
Solution: c
2nd element in each row. Sum up the digits of each number.
- 3 + 7 + 0 = 10
- 2 + 2 + 4 = 8
- 7 + 3 + 0 = 10
SO, 1+x = 10
Therefore x = 9
12.Four cars are hired at the rate of Rs. 6 per km plus the cost of diesel at Rs. 40 a litre. In this context, consider the details given in the following table:
Which car maintained the maximum average speed?
A.Car A
B.Car B
C.Car C
D.Car D
Solution: a
Four cars are hired at the rate of Rs. 6 per km plus the cost of diesel at Rs. 40 per liter
Let the distance traveled by cars A, B, C, and D be a, b, c, d respectively..
For car A, the total payment is given as 2120. Using the given rate, we can write the equation:
6 × a + 40 × (a/8) = 2120
11a = 2120
a = 2120/11
The average speed of car A is given by the formula:
a/20
Substituting the value of a, we get:
2120/(11 × 20) = 9.63
For car B, the total payment is given as 1950. Using the given rate, we can write the equation:
6 × b + 40 × (b/10) = 1950
10b = 1950
b = 195
The average speed of car B is given by the formula:
b/25
Substituting the value of b, we get:
195/25 = 7.8
For car C, the total payment is given as 2064. Using the given rate, we can write the equation:
6 × c + 40 × (c/9) = 2064
c = (9 × 1032)/47
The average speed of car C is given by the formula:
c/24
Substituting the value of c, we get:
(9 × 1032)/(47 × 24) = 8.23
For car D, the total payment is given as 1812. Using the given rate, we can write the equation:
6 × d + 40 × (d/11) = 1812
d = (11 × 906)/53
The average speed of car D is given by the formula:
d/22
Substituting the value of d, we get:
453/53 = 8.54
Comparing the average speeds of all the cars, we can see that car A has the maximum average speed, which is 9.63. Therefore, the answer is option (A) Car A.
13.Examine the following three figures in which the numbers follow a specific pattern:
The missing number (?) in the third figure above is
A.7
B.16
C.21
D.28
Solution: b
From the first two figures :
2 x 84 /12 =14
2 x 81/9 = 18
So,inr the third figure,
2 x 88/11 =x
Therefore x = 16
14.A cube has six numbers marked 1, 2, 3, 4, 5 and 6 on its faces. Three views of the cube are shown below:
What possible numbers can exist on the two faces marked A and B , respectively on the cube?
A.2 and 3
B.6 and 1
C.1 and 4
D.3 and 1
Solution: a
Direction for the following 5 (five) items:
Study the two figures given below and answer the five items that follow:
15.How many Physics professors belong to the age group 35 - 44?
A.18
B.16
C.14
D.12
Solution: b
Number of professors in physics = 40
Percentage of professors in age group 35 – 44 = 40%
Therefore the Physics professors belong to age group 35 – 44 is equal to 40% of 40 which is equal to 16
16.Which one of the following disciplines has the highest ratio of males to females?
A.Physics
B.Mathematics
C.Chemistry
D.Economics
Solution: A
The number of male professor in Physics = 32
The number of female professor in Physics = 8
Male : Female = 32 : 4
Male : Female = 4∶ 1 ----(A)
The number of male and female professors in Mathematics are 28 and 8 respectively.
Male : Female = 28∶ 8
Male∶ Female = 7∶ 2 ----(B)
The number of male and female professors in Chemistry are 16 and 22 respectively.
Male∶ Female = 16∶ 22
Male∶ Female = 8∶ 11 ----(C)
The number of male and female professors in Botany are 10 and 14 respectively.
Male∶ Female = 10∶ 14
Male∶ Female = 5∶ 7 ----(D)
The number of male and female professors in Psychology are 4 and 6 respectively.
Male∶ Female = 4∶ 6
Male∶ Female = 2∶ 3 ----(E)
The number of male and female professors in Economics are 24 and 8 respectively.
Male∶ Female = 24∶ 8
Male∶ Female = 3∶ 1 ----(F)
From equations (A), (B), (C), (D), (E) and (F) we can say that physics has the highest ratio of male and female.
16 What percentage of all Psychology professors are females?
(a) 40%
(b) 50%
(c) 60%
(d) 70%
Solution: c
No. of females psychology professor = 6
No. of males psychology professor = 4
The percentage of all Psychology professors are females is:
Number of females / total males and females multiplied by 100
=(6/10) x 100
= 60 percent
- If the number of female Physics professors in the age group 25 - 34 equals 25% of all the Physics professors in that age group, then what is the number of male Physics professors in the age group 25 - 34?
A.9
B.6
C.3
D.2
Solution: a
The number of male professors in the Physics discipline is 32
The number of female professors in the Physics discipline is 8.
The age distribution of Physics professors is as follows:
- 25-34 years: 30%
- 35-44 years: 40%
- 45-59 years: 20%
- 60-65 years: 10%
We need to find the number of male professors in the age group of 25-34.
To calculate this, we first determine the total number of professors in the age group of 25-34. Total number of professors in the Physics discipline is 32 (male) + 8 (female) = 40.
Next, we calculate the number of professors in the age group of 25-34 as a percentage of the total number of professors:
30% of 40 = (30/100) * 40 = 12
So, there are 12 professors in the age group of 25-34.
Since we know that 25% of all professors (male + female) in the age group of 25-34 are female, we can calculate the number of female professors:
Female = (1/4) * 12 = 3
Therefore, the number of male professors in the age group of 25-34 is:
Male = Total professors - Female professors = 12 - 3 = 9
Hence, there are 9 male professors in the age group of 25-34 in the Physics discipline.
17.If the Psychology professors in the University constitute 2% of all the professors in the University, then what is the number of professors in the University?
(a) 400
(b) 500
(c) 600
(d) 700
Solution: b
Let the number of professors in the university = a
According to question 2% of a = 10
So,
a = (10 x 100) / 2
Therefore a = 500
17.Consider the following figures:
Which one of the following figures would logically come in the 7th position indicated above by a question mark?
Solution: d
18.Four friends, A, B, C and D distribute some money among themselves in such a manner that A gets one less than B, C gets 5 more than D, D gets 3 more than B. Who gets the smallest amount?
A.A
B.B
C.C
D.D
Solution: a
A gets one less than B, so A < B.
C gets 5 more than D, so C > D.
D gets 3 more than B, so D > B.
Therefore, A < B < D < C.
A gets the smallest amount.
Directions for the following 4 (four) items:
Read the following statements and answer the four items that follow:
Five cities P, Q, R, S and T are connected by different modes of transport as follows:
P and Q are connected by boat as well as rail.
Sand R are connected by bus and boat. Q and T are connected by air only.
P and R are connected by boat only.
T and R are connected by rail and bus.
19.Which mode of transport would help one to reach R starting from Q, but without changing the mode of transport?
A.Boat
B.Rail
C.Bus
D.Air
Solution: a
The correct answer is A.
To reach R from Q without changing the mode of transport, one can take a boat from Q to P and then take a boat from P to R.
20.If a person visits each of the places starting from P and gets back to P, which of the following places must he visit twice?
A.Q
B.R
C.S
D.T
Solution: b
If a person visits each of the places starting from P and gets back to P, they must visit R twice. This is because R is the only city that is connected to P by two different modes of transport (boat and rail).
21.Which one of the following pairs of cities is connected by any of the routes directly without going to any other city?
A.P and T
B.T and S
C.Q and R
D.None of these
Solution: d
None of the pairs of cities is connected by any of the routes directly without going to any other city. To get from P to T, one must go through Q or R. To get from T to S, one must go through Q or R. To get from Q to R, one must go through P or T.
22.Between which two cities among the pairs of cities given below are there maximum travel options available?
A.Q and S
B.P and R
C.P and T
D.Q and R
Solution: b
The correct answer is B.
Between P and R, there are two travel options available: boat and rail. Between Q and S, there is only one travel option available: bus. Between P and T, there is only one travel option available: rail. Between Q and R, there is only one travel option available: boat.
Directions for the following 3 (three) items:
Read the following passage and answer the three items that follow:
A tennis coach is trying to put together a team of four players for the forthcoming tournament. For this 7 players are available: males A, Band C; and females W, X, Y and Z. All players have equal capability and at least 2 males will be there in the team. For a team of four, all players must be able to play with each other. But, B cannot play with W, C cannot play with Z and W cannot play with Y.
23.If Y is selected and B is rejected, the team will consist of which one of the following groups?
A.A, C, Wand Y
B.A, C, X and Y
C.A, C, Y and Z
D.A, W, Y and Z
Solution: b
The problem states that we have three males (A, B, and C) and four females (W, X, Y, and Z). We need to form a team of four members with at least two males, while also considering the given conditions:
- B cannot play with W.
- C cannot play with Z.
- W cannot play with Y.
To find the team that satisfies all conditions, we consider each possible combination. Let's analyze them one by one:
A, C, W, and Y: This team cannot be formed because W cannot play with Y. Thus, this combination is not valid.
A, C, X, and Y: This team can be formed as it includes at least two males, and all the conditions are satisfied. Therefore, this combination is valid.
A, C, Y, and Z: This team cannot be formed because C cannot play with Z. Thus, this combination is not valid.
A, W, Y, and Z: This team cannot be formed as it does not include at least two males. Also, W cannot play with Y. Thus, this combination is not valid.
Based on the analysis, the team that can be formed, satisfying all the conditions, is 'A, C, X, and Y'. Therefore, 'A, C, X, and Y' is the correct answer.
24.If B is selected and Y is rejected, the team will consist of which one of the following groups?
A.A, B, C and W
B.A, B, C and Z
C.A, B, C and X
D.A, W, Y and Z
Solution: c
If B is selected, W cannot be selected. So, options (a) and (d) are ruled out.
Since C cannot play with Z, option (b) is also ruled out.
Therefore option (c) is the correct answer.
25.If all the three males' are selected, then how many combinations of four member teams are possible?
A.1
B.2
C.3
D.4
Solution: b
Given conditions:
Males: A, B, and C
Females: W, X, Y, and Z
- B cannot play with W
- C cannot play with Z
- W cannot play with Y
To determine the number of combinations, we need to select 3 out of the 4 available females (W, X, Y, Z) since all three males will be selected. We can use the concept of combinations to calculate this.
The number of combinations of selecting r items out of a set of n items is given by the formula: nCr = n! / (r!(n-r)!)
In this case, we want to select 3 females out of the 4 available (W, X, Y, Z). So we have: 4C3 = 4! / (3!(4-3)!) = 4.
Therefore, there are 4 combinations of four-member teams possible if all three males (A, B, and C) are selected. These combinations are:
- A, B, C, and W (Not possible as B cannot play with W)
- A, B, C, and X (Possible)
- A, B, C, and Y (Possible)
- A, B, C, and Z (Not possible as C cannot play with Z)
Hence, the correct answer is 2.
26.The music director of a film wants to select four persons to work on different aspects of the composition of a piece of music. Seven persons are available for this work; they are Rohit, Tanya, Shobha, Kaushal, Kunal, Mukesh and Jaswant. Rohit and Tanya will not work together. Kunal and Shobha will not work together. Mukesh and Kunal want to work together.
Which of the following is the most acceptable group of people that can be selected by the music director?
A.Rohit, Shobha, Kunal and Kaushal
B.Tanya, Kaushal, Shobha and Rohit
C.Tanya, Mukesh, Kunal and Jaswant
D.Shobha, Tanya, Rohit and Mukesh
Solution: c
The correct answer is C.
Rohit and Tanya will not work together, so Rohit and Tanya cannot be selected together.
Kunal and Shobha will not work together, so Kunal and Shobha cannot be selected together.
Mukesh and Kunal want to work together, so Mukesh and Kunal should be selected together.
Therefore, the most acceptable group of people that can be selected by the music director is Tanya, Mukesh, Kunal and Jaswant.
29.Five people A, B, C, D and E are, seated about a round table, Every chair is spaced equidistant from adjacent chairs,
C is seated next to A.
A is seated two seats from D.
B is not seated next to A.
Which of the following must be true?
D is seated next to B.
E is seated next to A.
Select the correct answer from the codes given below:
A.I only
B.II only
C.Both I and II
D.Neither I nor II
Solution: c
The correct answer is C.
We know that C is seated next to A, A is seated two seats from D, and B is not seated next to A. This means that E must be seated next to A, and D must be seated next to B.
Directions for the following 3 (three) items:
Examine carefully the following statements and answer the three items that follow:
Out of four friends A, B, C and D, A and B play football and cricket, B and C play cricket and hockey,
A and D play basketball and football, C and D play hockey and basketball.
30.Who does not play hockey?
A.D
B.C
C.B
D.A
Solution: d
A plays football, basketball, and cricket.
B plays football, cricket, and hockey.
C plays cricket, hockey, and basketball.
D plays football, basketball, and hockey.
31.Who plays football, basketball and hockey?
A.D
B.C
C.B
D.A
Solution: c
33.Which game do B, C and D play?
A.Basketball
B.Hockey
C.Cricket
D.Football
Solution: b
34.Geeta is older than her cousin Meena, Meena's brother Bipin is older than Geeta. When Meena and Bipin visit Geeta, they like to play chess. Meena wins the game more often than Geeta. Based on the above information, four conclusions, as given below, have been made.
Which one of these logically follows from the information given above?
A.While playing chess with Geeta and Meena, Bipin often loses.
B.Geeta is the oldest among the three.
C.Geeta hates to 10 the game.
D.Meena is the youngest of the three.
Solution: d
We know that Bipin is older than Geeta, and Geeta is older than Meena. This means that Meena is the youngest of the three.
We also know that Meena wins the game more often than Geeta, but we do not know how often Bipin wins. Therefore, we cannot say for sure whether Bipin often loses, or whether Geeta hates to lose.
35.There are five hobby clubs in a college viz, photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day.
How many times do all the five groups meet on the same day within 180 days?
A.3
B.5
C.10
D.18
Solution: a
The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day.
The least common multiple of 2, 3, 4, 5, and 6 is 60.
Therefore, all the five groups meet on the same day every 60 days.
In 180 days, all the five groups meet on the same day 180 / 60 = 3 times.
36.A, B, C, D and E belong to five different cities P, Q, R, and T (not necessarily in that order). Each one of them comes from a different city. Further it is given that:
B and C do not belong to Q.
B and E do not belong to P and R.
A and C do not belong to R, Sand T.
D and E do not belong to Q and T.
Which one of the following statements is not correct?
A.C belongs to P
B.D belongs to R
C.A belongs to Q
D.B belongs to S
Solution: d
From statements 1 and 3, C does not belong to Q, R, S, and T. So, only one possibility is left - C belongs to P.
From statement 3, A does not belong to R, S, and T. So, A belongs to Q.
From statements 2 and 4, E does not belong to P, R, Q, and T. So, E belongs to S. B can not belong to S.
Therefore, B belongs to R.
So, the statement that is not correct is "B belongs to S".
37.Seven men, A, B, C, D, E, F and G are standing in a queue in that order. Each one is wearing a cap of a different colour like violet, indigo, blue, green, yellow, orange and red. D is able to see in front of him green and blue, but not violet. E can see violet and yellow, but not red. G can see caps of all colours other than orange.
If E is wearing an indigo coloured cap, then the colour of the cap worn by F is
A.Blue
B.Violet
C.Red
D.Orange
Solution: c
D is able to see green and blue, but not violet, so B and C wear green and blue, in either order.
E can see violet and yellow, but not red, so A wears violet and F wears yellow.
G can see all colors other than orange, so G wears orange.
E wears indigo, so D wears blue and C wears green.
Therefore, F wears red.
38.There are some balls of red, green and yellow colour lying on a table. There are as many red balls as there are yellow balls. There are twice as many yellow balls as there are green ones. The number of red balls
A.is equal to the sum of yellow and green balls.
B.is double the number of green balls.
C.is equal to yellow balls minus green balls.
D.cannot be ascertained.
Solution: b
There are as many red balls as there are yellow balls, so R = Y.
There are twice as many yellow balls as there are green ones, so Y = 2G.
Therefore, R = Y = 2G.
The number of red balls is double the number of green balls.
39.In a class of 45 students, a boy is ranked 20th. When two boys joined, his rank was dropped by one.
What is his new rank from the end?
A.25th
B.26th
C.27th
D.28th
Solution: c
The boy's rank is 20th in a class of 45 students. This means that there are 24 students behind him and 20 students ahead of him. When two boys joined the class, his rank dropped by one. This means that there are now 26 students behind him and 21 students ahead of him.
His new rank is 21st from the top, or 27th from the bottom.
40.A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 m ahead of the policeman, then
The time required for the policeman to catch the thief will be
A.2 min
B.3 min
C.4 min
D.6 min
Solution:b
The relative speed between the policeman and the thief is the difference between their speeds: 10 km/hr - 8 km/hr = 2 km/hr.
Since we have the relative speed in km/hr and the distance in meters, we need to convert the relative speed to m/s.
1 km/hr = 1000 m/3600 s = 5/18 m/s
So, the relative speed is 2 km/hr * (5/18 m/s) = 10/18 m/s = 5/9 m/s.
Now, we can calculate the time required for the policeman to catch the thief using the formula:
Time = Distance / Speed
Here, the distance is 100 meters, and the relative speed is 5/9 m/s.
Time = 100 m / (5/9 m/s) = 100 * (9/5) s = 180 s
Converting the time to minutes:
180 s = 180/60 min = 3 min
Therefore, the time required for the policeman to catch the thief is 3 minutes.
So, the correct answer is B. 3 min.
41.A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey,
what is the original speed of the train in km/hr?
A.24
B.33
C.42
D.66
Solution: c
Let x be the original speed of the train.
The time taken to travel 63 km at an average speed of x is 63/x.
The time taken to travel 72 km at an average speed of x+6 is 72/(x+6).
The total time taken to complete the journey is 3 hours.
Therefore, 63/x + 72/(x+6) = 3.
Solving for x, we get x = 42.
Therefore, the original speed of the train is 42 km/hr.
